Calculus of Variations and Geometric Measure Theory

M. Barchiesi - G. Lazzaroni - C. I. Zeppieri

A bridging mechanism in the homogenisation of brittle composites with soft inclusions

created by barchiesi on 24 Jan 2015
modified by lazzaroni on 29 Mar 2016


Published Paper

Inserted: 24 jan 2015
Last Updated: 29 mar 2016

Journal: SIAM J. Math. Anal.
Volume: 48
Pages: 1178-1209
Year: 2016


We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale $\varepsilon$ to obtain, in the limit as $\varepsilon$ tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.

Keywords: $\Gamma$-convergence, Free-discontinuity problems, fracture mechanics, multiscale analysis, homogenisation